Question: Simplify; express your answer in exponential form. Assume $y\neq 0, z\neq 0$. $\dfrac{{(y)^{2}}}{{(y^{3}z^{4})^{-1}}}$
Solution: To start, try working on the numerator and the denominator independently. In the numerator, we have ${y}$ to the exponent ${2}$ . Now ${1 \times 2 = 2}$ , so ${(y)^{2} = y^{2}}$ In the denominator, we can use the distributive property of exponents. ${(y^{3}z^{4})^{-1} = (y^{3})^{-1}(z^{4})^{-1}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(y)^{2}}}{{(y^{3}z^{4})^{-1}}} = \dfrac{{y^{2}}}{{y^{-3}z^{-4}}}$ Break up the equation by variable and simplify. $\dfrac{{y^{2}}}{{y^{-3}z^{-4}}} = \dfrac{{y^{2}}}{{y^{-3}}} \cdot \dfrac{{1}}{{z^{-4}}} = y^{{2} - {(-3)}} \cdot z^{- {(-4)}} = y^{5}z^{4}$.